Author | Protter, Philip. author |
---|---|

Title | Stochastic Integration and Differential Equations [electronic resource] : A New Approach / by Philip Protter |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1990 |

Connect to | http://dx.doi.org/10.1007/978-3-662-02619-9 |

Descript | X, 302 p. online resource |

SUMMARY

The idea of this book began with an invitation to give a course at the Third Chilean Winter School in Probability and Statistics, at Santiago de Chile, in July, 1984. Faced with the problem of teaching stochastic integration in only a few weeks, I realized that the work of C. Dellacherie [2] provided an outline for just such a pedagogic approach. I developed this into aseries of lectures (Protter [6]), using the work of K. Bichteler [2], E. Lenglart [3] and P. Protter [7], as well as that of Dellacherie. I then taught from these lecture notes, expanding and improving them, in courses at Purdue University, the University of Wisconsin at Madison, and the University of Rouen in France. I take this opportunity to thank these institut ions and Professor Rolando Rebolledo for my initial invitation to Chile. This book assumes the reader has some knowledge of the theory of stochastic processes, including elementary martingale theory. While we have recalled the few necessary martingale theorems in Chap. I, we have not provided proofs, as there are already many excellent treatments of martingale theory readily available (e. g. , Breiman [1], Dellacherie-Meyer [1,2], or Ethierยญ Kurtz [1]). There are several other texts on stochastic integration, all of which adopt to some extent the usual approach and thus require the general theory. The books of Elliott [1], Kopp [1], Metivier [1], Rogers-Williams [1] and to a much lesser extent Letta [1] are examples

CONTENT

I Preliminaries -- II Semimartingales and Stochastic Integrals -- III Semimartingales and Decomposable Processes -- IV General Stochastic Integration and Local Times -- V Stochastic Differential Equations -- References

Mathematics
Mathematical analysis
Analysis (Mathematics)
Probabilities
Applied mathematics
Engineering mathematics
Mathematics
Probability Theory and Stochastic Processes
Analysis
Appl.Mathematics/Computational Methods of Engineering